JEE Mathematics

Conic Sections (Parabola, Ellipse, Hyperbola): JEE Questions & Solutions

134 previous-year JEE Mathematics questions on Conic Sections (Parabola, Ellipse, Hyperbola), each with a worked step-by-step solution.

Advanced

Previous-year questions

  1. 01Let O be the vertex of the parabola x²=4y and Q be any point on it. Let the locus of the point P, which divides the line segment OQ…MCQMediumJEE 2026
  2. 02Let the foci of a hyperbola coincide with the foci of the ellipse x²/36 + y²/16 = 1. If the eccentricity of the hyperbola is 5, then the…MCQMediumJEE 2026
  3. 03If the line ax + 4y = √7, where a ∈ ℝ, touches the ellipse 3x² + 4y² = 1 at the point P in the first quadrant, then one of the focal…MCQMediumJEE 2026
  4. 04Let one end of a focal chord of the parabola y² = 16x be (16, 16). If P(α, β) divides this focal chord internally in the ratio 5: 2, then…MCQMediumJEE 2026
  5. 05Let y² = 12x be the parabola with its vertex at O. Let P be a point on the parabola and A be a point on the x-axis such that ∠ OPA = 90^°.…MCQMediumJEE 2026
  6. 06If the chord joining the points P₁(x₁, y₁) and P₂(x₂, y₂) on the parabola y² = 12x subtends a right angle at the vertex of the parabola,…MCQMediumJEE 2026
  7. 07If the line ax + 2y = 1, where a ∈ ℝ, does not meet the hyperbola x² - 9y² = 9, then a possible value of a is:MCQMediumJEE 2026
  8. 08Let P(10, 2√15) be a point on the hyperbola x²/a² - y²/b² = 1, whose foci are S and S'. If the length of its latus rectum is 8, then the…MCQMediumJEE 2026
  9. 09Let the locus of the mid-point of the chord through the origin O of the parabola y² = 4x be the curve S. Let P be any point on S. Then the…MCQMediumJEE 2026
  10. 10Let S and S' be the foci of the ellipse x²/25 + y²/9 = 1 and P(α,β) be a point on the ellipse in the first quadrant. If (SP)² + (S'P)² - SP…MCQMediumJEE 2026
  11. 11Let the line y - x = 1 intersect the ellipse x²/2 + y²/1 = 1 at the points A and B. Then the angle made by the line segment AB at the…MCQMediumJEE 2026
  12. 12Let the domain of f(x) = log₃ log₅ log₇ (9x - x² - 13) be (m, n). Let the hyperbola x²/a² - y²/b² = 1 have eccentricity n/3 and latus…MCQMediumJEE 2026
  13. 13An equilateral triangle OAB is inscribed in the parabola y² = 4x with the vertex O at the vertex of the parabola. Then the minimum distance…MCQMediumJEE 2026
  14. 14If the points of intersection of the ellipses x² + 2y² - 6x - 12y + 23 = 0 and 4x² + 2y² - 20x - 12y + 35 = 0 lie on a circle of radius r…MCQMediumJEE 2026
  15. 15Let PQ be a chord of the hyperbola x²/4 - y²/b² = 1, perpendicular to the x-axis, such that OPQ is an equilateral triangle, O being the…MCQMediumJEE 2026
  16. 16Let each of the two ellipses E₁:x²/a²+y²/b²=1 (a>b) and E₂:x²/A²+y²/B²=1 (A<B) have eccentricity 4/5. Let the lengths of the latus recta of…MCQMediumJEE 2026
  17. 17Let the length of the latus rectum of an ellipse x²/a²+y²/b²=1 (a>b) be 30. If its eccentricity is the maximum value of the function…MCQMediumJEE 2026
  18. 18Let the image of parabola x²=4y in the line x-y=1 be (y+a)²=b(x-c), where a,b,c∈ℕ. Then a+b+c is equal toMCQMediumJEE 2026
  19. 19Let (h,k) lie on the circle C:x²+y²=4 and the point (2h+1, 3k+2) lie on an ellipse with eccentricity e. Then the value of 5/e² is equal toNVAMediumJEE 2026
  20. 20Let ABC be an equilateral triangle with orthocenter at the origin and the side BC lying on the line x+2√2 y=4. If the coordinates of the…MCQMediumJEE 2026
  21. 21For some θ∈(0,π/2), let the eccentricity and the length of the latus rectum of the hyperbola x²-y²sec²θ=8 be e₁ and l₁, respectively, and…NVAMediumJEE 2026
  22. 22Let the ellipse E: x²/144+y²/169=1 and the hyperbola H: x²/16-y²/λ²=-1 have the same foci. If e and L respectively denote the eccentricity…MCQMediumJEE 2026
  23. 23An ellipse has its centre at (1,-2), one focus at (3,-2) and one vertex at (5,-2). Then the length of its latus rectum is:MCQEasyJEE 2026
  24. 24Let A be the focus of the parabola y²=8x. Let the line y=mx+c intersect the parabola at two distinct points B and C. If the centroid of…MCQMediumJEE 2026
  25. 25Let the parabola y = x² + px - 3 meet the coordinate axes at the points P, Q and R. If the circle C with centre at (-1, -1) passes through…MCQMediumJEE 2025
  26. 26Let the foci of a hyperbola be (1, 14) and (1, -12). If it passes through the point (1, 6), then the length of its latus-rectum is:MCQMediumJEE 2025
  27. 27Let P(4, 4√3) be a point on the parabola y² = 4ax and PQ be a focal chord of the parabola. If M and N are the foot of the perpendiculars…MCQMediumJEE 2025
  28. 28Let E: x²/a² + y²/b² = 1, a > b and H: x²/A² - y²/B² = 1. Let the distance between the foci of E and the foci of H be 2√3. If a - A = 2,…MCQMediumJEE 2025
  29. 29Let A(6,8), B(10cosα, -10sinα), and C(-10sinα, 10cosα) be the vertices of a triangle. If L(a,9) and G(h,k) be its orthocenter and centroid…NVAMediumJEE 2025
  30. 30If the line 3x - 2y + 12 = 0 intersects the parabola 4y = 3x² at the points A and B, then at the vertex of the parabola, the line segment…MCQMediumJEE 2025
  31. 31Let the area of a triangle △ PQR with vertices P(5, 4), Q(-2, 4), and R(a, b) be 35 square units. If its orthocenter and centroid are O(2,…MCQMediumJEE 2025
  32. 32Let the circle C touch the line x - y + 1 = 0, have the center on the positive x-axis, and cut off a chord of length 4/√13 along the line…NVAMediumJEE 2025
  33. 33A rod of length eight units moves such that its ends A and B always lie on the lines x - y + 2 = 0 and y + 2 = 0, respectively. If the…MCQMediumJEE 2025
  34. 34Let the shortest distance from (a, 0), where a > 0, to the parabola y² = 4x be 4. Then the equation of the circle passing through the point…MCQMediumJEE 2025
  35. 35The length of the chord of the ellipse: x²/4 + y²/2 = 1, whose mid-point is ( 1, 1/2), is:MCQMediumJEE 2025
  36. 36The focus of the parabola y² = 4x + 16 is the center of the circle C with radius 5. If the values of λ, for which C passes through the…NVAMediumJEE 2025
  37. 37Let the product of the focal distances of the point ( √3, 1/2) on the ellipse x²/a² + y²/b² = 1, (a > b), be 7/4. Then the absolute…MCQMediumJEE 2025
  38. 38If the equation of the parabola with vertex ( 3/2, 3) and the directrix x + 2y = 0 is α x² + β y² - γ xy - 30x - 60y + 225 = 0, then α + β…MCQMediumJEE 2025
  39. 39The equation of the chord of the ellipse x²/25 + y²/16 = 1, whose mid-point is (3, 1) is:MCQMediumJEE 2025
  40. 40Let H₁: x²/a² - y²/b² = 1 and H₂: -x²/A² + y²/B² = 1 be two hyperbolas having lengths of latus rectums 15√2 and 12√5 respectively. Let…NVAMediumJEE 2025
  41. 41Let ABCD be a trapezium whose vertices lie on the parabola y² = 4x. Let the sides AD and BC of the trapezium be parallel to the y-axis. If…MCQMediumJEE 2025
  42. 42If A and B are the points of intersection of the circle x² + y² - 8x = 0 and the hyperbola x²/9 - y²/4 = 1, and a point P moves on the line…MCQMediumJEE 2025
  43. 43If the midpoint of a chord of the ellipse x²/9 + y²/4 = 1 is ( √2, 4/3), and the length of the chord is 2√α/3, then α is:MCQMediumJEE 2025
  44. 44Let A and B be the two points of intersection of the line y + 5 = 0 and the mirror image of the parabola y² = 4x with respect to the line x…NVAMediumJEE 2025
  45. 45Let the ellipse E₁: x²/a² + y²/b² = 1, a > b and E₂: x²/A² + y²/B² = 1, A < B, have the same eccentricity 1/√3. Let the product of their…MCQHardJEE 2025
  46. 46Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersect at…MCQMediumJEE 2025
  47. 47Let the line x + y = 1 meet the axes of x and y at A and B, respectively. A right-angled triangle AMN is inscribed in the triangle OAB,…MCQMediumJEE 2025
  48. 48If α x + β y = 109 is the equation of the chord of the ellipse x²/9 + y²/4 = 1 whose midpoint is (5/2, 1/2), then α + β is equal to:MCQMediumJEE 2025
  49. 49Let y² = 12x be the parabola and S its focus. Let PQ be a focal chord of the parabola such that (SP)(SQ) = 147/4. Let C be the circle…NVAMediumJEE 2025
  50. 50Let one focus of the hyperbola H: x²/a² - y²/b² = 1 be at (√10, 0) and the corresponding directrix be x = 9/√10. If e and l are…MCQMediumJEE 2025
  51. 51If S and S' are the foci of the ellipse x²/18 + y²/9 = 1 and P be a point on the ellipse, then min(SP · S'P) + max(SP · S'P) is equal to:MCQMediumJEE 2025
  52. 52Let the focal chord PQ of the parabola y² = 4x make an angle of 60^° with the positive x-axis, where P lies in the first quadrant. If the…MCQMediumJEE 2025
  53. 53If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse…MCQMediumJEE 2025
  54. 54Let the point P of the focal chord PQ of the parabola y² = 16x be (1, -4). If the focus of the parabola divides the chord PQ in the ratio…MCQMediumJEE 2025
  55. 55Let A(4, -2), B(1, 1) and C(9, -3) be the vertices of a triangle ABC. Then the maximum area of the parallelogram AFDE, formed with vertices…NVAMediumJEE 2025
  56. 56A line passing through the point P(√5, √5) intersects the ellipse x²/36 + y²/25 = 1 at A and B such that (PA).(PB) is maximum. Then 5(PA² +…MCQMediumJEE 2025
  57. 57The radius of the smallest circle which touches the parabolas y = x² + 2 and x = y² + 2 isMCQMediumJEE 2025
  58. 58Let the product of the focal distances of the point P(4, 2√3) on the hyperbola H: x²/a² - y²/b² = 1 be 32. Let the length of the conjugate…NVAMediumJEE 2025
  59. 59Let C be the circle of minimum area enclosing the ellipse E: x²/a² + y²/b² = 1 with eccentricity 1/2 and foci (± 2, 0). Let PQR be a…MCQMediumJEE 2025
  60. 60The shortest distance between the curves y² = 8x and x² + y² + 12y + 35 = 0 is:MCQMediumJEE 2025
  61. 61If the equation of the hyperbola with foci (4, 2) and (8, 2) is 3x² - y² - α x + β y + γ = 0, then α + β + γ is equal toNVAMediumJEE 2025
  62. 62Let the three sides of a triangle are on the lines 4x - 7y + 10 = 0, x + y = 5, and 7x + 4y = 15. Then the distance of its orthocenter from…MCQEasyJEE 2025
  63. 63The length of the latus-rectum of the ellipse, whose foci are (2, 5) and (2, -3) and eccentricity is 4/5, isMCQEasyJEE 2025
  64. 64Let C be the circle x² + (y - 1)² = 2, E₁ and E₂ be two ellipses whose centres lie at the origin and major axes lie on the x-axis and…NVAMediumJEE 2025
  65. 65The axis of a parabola is the line y = x and its vertex and focus are in the first quadrant at distances √2 and 2√2 units from the origin,…MCQMediumJEE 2025
  66. 66A line passing through the point A(-2, 0), touches the parabola P: y² = x - 2 at the point B in the first quadrant. The area of the region…MCQMediumJEE 2025
  67. 67Let the sum of the focal distances of the point P(4, 3) on the hyperbola x²/a² - y²/b² = 1 be 8√(5/3). If for H, the length of the latus…MCQMediumJEE 2025
  68. 68Let for two distinct values of p, the lines y = x + p touch the ellipse E: x²/4² + y²/3² = 1 at the points A and B. Let the line y = x…MCQMediumJEE 2025
  69. 69The center of a circle C is at the center of the ellipse E: x²/a² + y²/b² = 1, where a > b. Let C pass through the foci F₁ and F₂ of E such…MCQHardJEE 2025
  70. 70Let P be the parabola, whose focus is (-2, 1) and directrix is 2x + y + 2 = 0. Then the sum of the ordinates of the points on P, whose…MCQMediumJEE 2025
  71. 71Consider the hyperbola x²/a² - y²/b² = 1, having one of its foci at P(-3, 0). If the latus rectum through its other focus subtends a right…NVAMediumJEE 2025
  72. 72Let A = {(α, β) ∈ ℝ × ℝ: |α - 1| ≤ 4 and |β - 5| ≤ 6} and B = {(α, β) ∈ ℝ × ℝ: 16(α - 2)² + 9(β - 6)² ≤ 144}. Then:MCQEasyJEE 2025
  73. 73Let the length of a latus rectum of an ellipse x²/a² + y²/b² = 1 be 10. If its eccentricity is the minimum value of the function f(t) = t²…MCQMediumJEE 2025
  74. 74Let e₁ and e₂ be the eccentricities of the ellipse x²/b² + y²/25 = 1 and the hyperbola x²/16 - y²/b² = 1, respectively. If b < 5 and e₁ e₂…MCQMediumJEE 2025
  75. 75Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2a and 2b, respectively, and one focus and the…NVAMediumJEE 2025
  76. 76Let the ellipse 3x² + py² = 4 pass through the centre C of the circle x² + y² - 2x - 4y - 11 = 0 of radius r. Let f₁, f₂ be the focal…MCQMediumJEE 2025
  77. 77Let a be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle α with the positive x-axis and the…MCQMediumJEE 2025
  78. 78Let r be the radius of the circle, which touches the x-axis at point (a, 0), a < 0 and the parabola y² = 9x at the point (4, 6). Then r is…NVAMediumJEE 2025
  79. 79If the shortest distance of the parabola y² = 4x from the centre of the circle x² + y² - 4x - 16y + 64 = 0 is d, then d² is equal to:MCQMediumJEE 2024
  80. 80The length of the chord of the ellipse x²/25 + y²/16 = 1, with midpoint (1, 2/5), is:MCQMediumJEE 2024
  81. 81If e₁ is the eccentricity of the hyperbola x²/16 - y²/9 = 1 and e₂ is the eccentricity of the ellipse x²/a² + y²/b² = 1, which passes…MCQMediumJEE 2024
  82. 82Let (5, a/4) be the circumcenter of a triangle with vertices A(a, -2), B(a, 6), and C(a/4, -2). Let α denote the circumradius, β the area,…MCQMediumJEE 2024
  83. 83If the points of intersection of two distinct conics x² + y² = 4b and x²/16 + y²/b² = 1 lie on the curve y² = 3x², then 3√3 times the area…MCQMediumJEE 2024
  84. 84Let P(α, β) be a point on the parabola y² = 4x. If P also lies on the chord of the parabola x² = 8y whose midpoint is (1, 5/4), then (α -…NVAMediumJEE 2024
  85. 85If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is:MCQEasyJEE 2024
  86. 86Let the latus rectum of the hyperbola x²/9 - y²/b² = 1 subtend an angle of π/3 at the center of the hyperbola. If b² is equal to l/m(1+√n),…NVAMediumJEE 2024
  87. 87Let A(10, 0) and B(0, β) be points on the line 5x + 7y = 50. Let P divide AB in the ratio 7:3. Let 3x-25 = 0 be a directrix of the ellipse…MCQMediumJEE 2024
  88. 88Let P be a point on the hyperbola H: x²/9 - y²/4 = 1, in the first quadrant such that the area of the triangle formed by P and the two foci…MCQMediumJEE 2024
  89. 89The area of the region enclosed by the parabola (y-2)² = x-1, the line x-2y+4 = 0, and the positive coordinate axes is:NVAMediumJEE 2024
  90. 90If the foci of a hyperbola are the same as that of the ellipse x²/9 + y²/25 = 1 and the eccentricity of the hyperbola is 15/8 times the…MCQMediumJEE 2024
  91. 91Let the foci and length of the latus rectum of an ellipse x²/a² + y²/b² = 1, a > b be (± 5, 0) and √50, respectively. Then, the square of…MCQMediumJEE 2024
  92. 92Let P be a parabola with vertex (2, 3) and directrix 2x + y = 6. Let an ellipse E with eccentricity 1/√2 pass through the focus of P. The…MCQMediumJEE 2024
  93. 93Let P be a point on the ellipse x²/9 + y²/4 = 1. Let the line passing through P and parallel to the y-axis meet the circle x² + y² = 9 at…MCQMediumJEE 2024
  94. 94The vertices of a triangle are A(-1, 3), B(-2, 2), and C(3, -1). A new triangle is formed by shifting the sides of the triangle one unit…MCQMediumJEE 2024
  95. 95Let C be the circle of minimum area touching the parabola y = 6 - x² and the lines y = √3|x|. Then, which one of the following points lies…MCQMediumJEE 2024
  96. 96The parabola y² = 4x divides the area of the circle x² + y² = 5 in two parts. The area of the smaller part is:MCQMediumJEE 2024
  97. 97The area (in square units) of the region enclosed by the ellipse x² + 3y² = 18 in the first quadrant below the line y = x is:MCQMediumJEE 2024
  98. 98Let the foci of a hyperbola H coincide with the foci of the ellipse E: (x-1)²/100 + (y-1)²/75 = 1, and the eccentricity of the hyperbola H…MCQMediumJEE 2024
  99. 99Two vertices of a triangle ABC are A(3,-1) and B(-2, 3), and its orthocenter is P(1, 1). If the coordinates of the point C are (α, β) and…MCQMediumJEE 2024
  100. 100The equations of the sides AB and AC of a triangle ABC are: (λ + 1)x + λ y = 4 and λ x + (1 - λ)y + λ = 0, respectively. Its vertex A is on…MCQMediumJEE 2023
  101. 101The distance of the point (6, -2√2) from the common tangent y = mx + c, m > 0, of the curves x = 2y² and x = 1 + y² is:MCQMediumJEE 2023
  102. 102The vertices of a hyperbola H are (±6, 0) and its eccentricity is √5/2. Let N be the normal to H at a point in the first quadrant and…NVAMediumJEE 2023
  103. 103The equations of two sides of a variable triangle are x = 0 and y = 3, and its third side is a tangent to the parabola y² = 6x. The locus…MCQMediumJEE 2023
  104. 104Let T and C respectively be the transverse and conjugate axes of the hyperbola 16x² - y² + 64x+ 4y + 44 = 0. Then the area of the region…MCQMediumJEE 2023
  105. 105If the tangent at a point P on the parabola y² = 3x is parallel to the line x + 2y = 1, and the tangents at the points Q and R on the…MCQMediumJEE 2023
  106. 106A triangle is formed by the tangents at the point (2, 2) on the curves y² = 2x and x² + y² = 4x, and the line x + y + 2 = 0. If r is the…NVAMediumJEE 2023
  107. 107If P(h,k) be a point on the parabola x = 4y², which is nearest to the point Q(0, 33), then the distance of P from the directrix of the…MCQMediumJEE 2023
  108. 108Let A be a point on the x-axis. Common tangents are drawn from A to the curves x² + y² = 8 and y² = 16x. If one of these tangents touches…MCQMediumJEE 2023
  109. 109Let y = f(x) represent a parabola with focus ( -1/2, 0) and directrix y = -1/2. Then S = { x ∈ ℝ: tan⁻¹ ( √f(x)) + sin⁻¹ ( √(f(x) + 1)) =…MCQMediumJEE 2023
  110. 110The set of all values of a² for which the line x + y = 0 bisects two distinct chords drawn from a point P( (1 + a)/2, (1 - a)/2) on the…MCQMediumJEE 2023
  111. 111Let H be the hyperbola, whose foci are (1 ± √2, 0) and eccentricity is √2. Then the length of its latus rectum is:MCQEasyJEE 2023
  112. 112Let S be the set of all a ∈ ℕ such that the area of the triangle formed by the tangent at the point P(b, c), b, c ∈ ℕ on the parabola y² =…NVAMediumJEE 2023
  113. 113Let P(x₀, y₀) be the point on the hyperbola 3x² - 4y² = 36, which is nearest to the line 3x + 2y = 1. Then √2 (y₀ - x₀) is equal to:MCQMediumJEE 2023
  114. 114The line x = 8 is the directrix of the ellipse E: x²/a² + y²/b² = 1 with the corresponding focus (2, 0). If the tangent to E at the point P…NVAMediumJEE 2023
  115. 115If the x-intercept of a focal chord of the parabola y² = 8x + 4y + 4 is 3, then the length of this chord is equal to.NVAMediumJEE 2023
  116. 116Let the tangents to the curve x² + 2x - 4y + 9 = 0 at the point P(1, 3) on it meet the y-axis at A. Let the line passing through P and…NVAMediumJEE 2023
  117. 117In a group of 100 persons, 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of…MCQMediumJEE 2023
  118. 118Let the eccentricity of an ellipse x²/a² + y²/b² = 1 be reciprocal to that of the hyperbola 2x² - 2y² = 1. If the ellipse intersects the…NVAMediumJEE 2023
  119. 119Let R be the focus of the parabola y² = 20x and the line y = mx + c intersect the parabola at two points P and Q. Let the point G(10, 10)…MCQMediumJEE 2023
  120. 120Let the ellipse E: x² + 9y² = 9 intersect the positive x- and y-axes at the points A and B respectively. Let the major axis of E be a…MCQMediumJEE 2023
  121. 121Let a common tangent to the curves y² = 4x and (x - 4)² + y² = 16 touch the curves at the points P and Q. Then (PQ)² is equal to:NVAMediumJEE 2023
  122. 122Let a circle of radius 4 be concentric to the ellipse 15x² + 19y² = 285. Then the common tangents are inclined to the minor axis of the…MCQMediumJEE 2023
  123. 123Consider ellipse E_k: k x² + k² y² = 1, for k = 1, 2, …, 20. Let C_k be the circle which touches the four chords joining the end points…MCQMediumJEE 2023
  124. 124Let Hₙ: x²/(1 + n) - y²/(3 + n) = 1, n ∈ ℕ. Let k be the smallest even value of n such that the eccentricity of H_k is a rational number.…MCQMediumJEE 2023
  125. 125If the radius of the largest circle with centre (2, 0) inscribed in the ellipse x² + 4y² = 36 is r, then 12r² is equal to:MCQMediumJEE 2023
  126. 126Let the tangent to the parabola y² = 12x at the point (3, α) be perpendicular to the line 2x + 2y = 3. Then the square of the distance of…NVAMediumJEE 2023
  127. 127Let P( 2√3/√7, 6/√7), Q, R, and S be four points on the ellipse 9x² + 4y² = 36. Let PQ and RS be mutually perpendicular and pass through…MCQMediumJEE 2023
  128. 128If the point (α, 7√3/3) lies on the curve traced by the mid-points of the line segments of the lines xcosθ + ysinθ = 7, θ ∈ (0, π/2),…MCQMediumJEE 2023
  129. 129Let PQ be a focal chord of the parabola y² = 36x of length 100, making an acute angle with the positive x-axis. Let the ordinate of P be…MCQMediumJEE 2023
  130. 130Let the tangent and normal at the point ( 3√3, 1) on the ellipse x²/36 + y²/4 = 1 meet the y-axis at the points A and B respectively. Let…MCQMediumJEE 2023
  131. 131Let (α, β) be the centroid of the triangle formed by the lines 15x - y = 82, 6x - 5y = -4 and 9x + 4y = 17. Then α + 2β and 2α - β are the…MCQMediumJEE 2023
  132. 132The foci of a hyperbola are (± 2, 0) and its eccentricity is 3/2. A tangent, perpendicular to the line 2x + 3y - 6 = 0, is drawn at a point…NVAMediumJEE 2023
  133. 133If (α,β) is the orthocenter of the triangle ABC with vertices A(3,-7), B(-1,2), C(4,5), then 9α-6β+60 is equal toMCQMediumJEE 2023
  134. 134Let an ellipse with centre (1,0) and latus rectum of length 1/2 have its major axis along the x-axis. If its minor axis subtends an angle…NVAMediumJEE 2023

Frequently asked questions

Our bank has 134 previous-year JEE Mathematics questions tagged to Conic Sections (Parabola, Ellipse, Hyperbola), drawn from JEE papers between 2023 and 2026, including 24 from 2026 alone. Each comes with a full step-by-step solution.

Conic Sections (Parabola, Ellipse, Hyperbola) is rated Advanced overall for JEE Mathematics. The PYQs on this page break down as 126 medium, 6 easy, 2 hard.

Of the 134 previous-year questions on Conic Sections (Parabola, Ellipse, Hyperbola), 105 are multiple-choice (MCQ) and 29 are numerical-value (NVA) questions.

Based on recent paper analysis, Conic Sections (Parabola, Ellipse, Hyperbola) is worth about 8 marks in JEE Main. It sits in Coordinate Geometry, a Class 11 Mathematics chapter.

More Coordinate Geometry topics

Circle Equation & Properties40Straight Line Equations32Basics: Distance, Section Formula, Locus8Slope & Angle Between Lines3Pair of Straight Lines1

Master Conic Sections (Parabola, Ellipse, Hyperbola) with AI-adaptive practice.

Practice unlimited Conic Sections (Parabola, Ellipse, Hyperbola) questions, track your mastery, and get every step explained by an AI tutor.

Start free trial